My dough is always so sticky, I can barely knead it (i.e. there is so much stuff stuck to my fingers that I tend to lose patience...). Should I add more flour?
The result is a good, bud dense bread. Not great yet...
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Soda bread is traditionally, a dense loaf, of relatively flavorless bread. I like it, my friend's grandmother made her grandmother's when I would go to his house, and it always was a hit. So I think you're doing things right. If you desire a lighter crumb (texture) try using cake or pastry flour as it contains less protein, thus yielding less gluten, this yielding a lighter crumb.
If this is a soda bread, I believe you should be stirring, not kneading -- treating it like a muffin, not a yeast bread. Then you can let the mixer or stirrer get sticky, and not your hands.
Here's Merrill's recipe for soda bread. Click on the slideshow link and you can see the exact texture of the dough. it doesn't look sticky at all. It's great - I've made it a few times.